Successive derivatives of the Zeta function evaluated at x=2 round to (-1)^n * n!, for the nth derivative, and converge with increasing n. For example, in Mathematica, Derivative[5][Zeta][2] = -120.000824333. A direct formula for the nth derivative of Zeta at x=2 is: (-1)^n*Sum_{k>=1} Log(k)^n/k^2. See also A201994 and A201995. The values of successive derivatives of Zeta(x) as x->1 are given by A252898, and are also related to the factorials. - Richard R. Forberg, Dec 30 2014